๐ช๐ต๐ ๐๐ถ๐ป๐ฒ๐ฎ๐ฟ ๐ฅ๐ฒ๐ด๐ฟ๐ฒ๐๐๐ถ๐ผ๐ป ๐๐ ๐จ๐ป๐๐๐ถ๐๐ฎ๐ฏ๐น๐ฒ ๐ณ๐ผ๐ฟ ๐๐ถ๐ป๐ฎ๐ฟ๐ ๐๐น๐ฎ๐๐๐ถ๐ณ๐ถ๐ฐ๐ฎ๐๐ถ๐ผ๐ป?
While linear regression can provide continuous output values, which may seem suitable for binary classification, it is not ideal for this purpose. Here are two key reasons why:
๐ก๐ผ๐ป-๐ฑ๐ถ๐ณ๐ณ๐ฒ๐ฟ๐ฒ๐ป๐๐ถ๐ฎ๐ฏ๐ถ๐น๐ถ๐๐ ๐ฎ๐ ๐๐ต๐ฒ ๐ง๐ต๐ฟ๐ฒ๐๐ต๐ผ๐น๐ฑ: Linear regression typically uses a threshold to classify data, but this threshold function is not differentiable at the decision boundary. This lack of smoothness makes optimization difficult, particularly when using gradient-based methods like gradient descent.
๐ฆ๐ฒ๐ป๐๐ถ๐๐ถ๐๐ถ๐๐ ๐๐ผ ๐ข๐๐๐น๐ถ๐ฒ๐ฟ๐: Linear regression is sensitive to outliers in the data, which can significantly affect the model's performance. Since the continuous output can range from negative to positive infinity, outliers can distort the decision boundary, leading to inaccurate classifications.
To address these issues, the threshold function (equation of separation plane) can be passed by a ๐๐ถ๐ด๐บ๐ผ๐ถ๐ฑ ๐ณ๐๐ป๐ฐ๐๐ถ๐ผ๐ป, which maps the output to a probability value in the range [0, 1]. The sigmoid function ensures that the model is not sensitive to outliers and provides a smooth, differentiable output for optimization. The result is a more reliable classification model for binary outcomes.
This transformation allows models like logistic regression to perform binary classification more effectively than linear regression.
For detailed understanding, go through this video:
I made the code for the animation public for further exploration: https://github.com/pritkudale/Code_for_LinkedIn/blob/main/Logistic_vs_linear_regression_for_binary_classification.ipynb
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